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Question Number 75627 by liki last updated on 14/Dec/19

Answered by $@ty@m123 last updated on 14/Dec/19

$$\mathit{I}\mathit{n}\mathit{i}\mathit{t}\mathit{i}\mathit{a}\mathit{l}\mathit{l}\mathit{y},$$$$Length=l$$$$Breadth=b$$$$\therefore Diagonal\mathit{d}=\sqrt{l^2+b^2}......\left(1\right)$$$$\mathit{A}\mathit{f}\mathit{t}\mathit{e}\mathit{r}\mathit{i}\mathit{n}\mathit{c}\mathit{e}\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathit{s}\mathit{b}\mathit{y}10\mathrm{\%},$$$$Length=l(1+\frac{10}{100})=\frac{110}{100}l=\frac{11}{10}l$$$$Breadth=b(1+\frac{10}{100})=\frac{110}{100}b=\frac{11}{10}b$$$$\therefore Diagonal\mathit{D}=\sqrt{{\left(\frac{11}{10}l\right)}^2+{\left(\frac{11}{10}b\right)}^2}$$$$\Rightarrow \mathit{D}=\frac{11}{10}\sqrt{l^2+b^2}.......\left(2\right)$$$$\therefore \mathit{P}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}\mathit{i}\mathit{n}\mathit{c}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathit{i}\mathit{n}\mathit{d}\mathit{i}\mathit{a}\mathit{g}\mathit{o}\mathit{n}\mathit{a}\mathit{l}$$$$=\frac{D-d}{d}\times 100$$$$=\frac{(\frac{11}{10}\sqrt{l^2+b^2}-\sqrt{l^2+b^2})}{\sqrt{l^2+b^2}}\times 100$$$$=\frac{(\frac{11}{10}-1)\sqrt{l^2+b^2})}{\sqrt{l^2+b^2}}\times 100$$$$=\frac{11-10}{10}\times 100$$$$=\frac{1}{10}\times 100$$$$=10\mathrm{\%}$$

Commented by liki last updated on 14/Dec/19

$$....\mathit{T}\mathit{h}\mathit{a}\mathit{n}\mathit{k}\mathit{y}\mathit{o}\mathit{u}\mathit{s}\mathit{i}\mathit{r}\mathit{b}\mathit{e}\mathit{b}\mathit{l}\mathit{e}\mathit{s}\mathit{s}\mathit{e}\mathit{d}$$

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